In the given figure, the arms of two angles are parallel.
If∠ABC = 70º, then find ∠DEF.

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$60^{\circ}$

$80^{\circ}$

$70^{\circ}$

$90^{\circ}$

answer is B.

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Detailed Solution

Given, The arms of two angles are parallel.

AB $∥$ DE

BC $∥$ EF

AB is parallel to DE. BC is a transversal. By using the property that when a pair of parallel lines are intersected by a transversal the pairs of corresponding angles are equal.

∠ABC = ∠DGC

∠DGC = $70^{\circ}$ (Given, ∠ABC = $70^{\circ}$ )

BC is parallel to EF. DE is a transversal. By using the property that when a pair of parallel lines are intersected by a transversal the pairs of corresponding angles are equal.

∠DGC = ∠DEF

∠DEF = $70^{\circ}$

$∴$ ∠DEF = ∠DGC = $70^{\circ}$ .

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